The 24-year-old landed heavily during South Korea's World Cup qualifying match with Qatar in Doha on Tuesday, and scans have since confirmed that he suffered a fracture to his right forearm.
No timeframe has been given on the attacker's recovery, but the injury is likely to see Son miss Tottenham's pre-season tour to the United States at the end of July.
"The South Korea international sustained the injury after landing on his arm during his national team's World Cup qualifying match against Qatar in Doha on Tuesday, with further assessment and scans confirming that he has sustained a fracture," read a statement on the club's official website.
"Son will continue to be monitored by our medical staff ahead of a return to action next season."
Son scored 21 goals in 47 appearances across all competitions last season - the most prolific goalscoring season of his career.